Extruding to particular thickness on an angle
You can get very close by:


Setting your transform orientation to 'Normal'
Setting your snap to 'Edge', Active'
In Edit/Vertex mode, (the pair of vertices selected) Extrude in Z Z by a numerically entered depth.
Translate the new edge in Y Y until the active vertex at one end 'snaps' to the wall.


But, it's not a true snap. The move is constrained, but the snap projection isn't. You can get very close by zooming in, and eyeballing the 'bullseye' of the snap range circle. Blender's snapping system is lacking, here.

You can install and use the built-in add-on  - 'Mesh:Tiny CAD' to make a true, accurate projection of the new, extruded edge to its intersection with the wall, but only if they're part of the same object, or you construct a new edge from the wall as a guide, which is part of the same object.